(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     28102,        835]
NotebookOptionsPosition[     26866,        793]
NotebookOutlinePosition[     27210,        808]
CellTagsIndexPosition[     27167,        805]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[""], "Input"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"symbpow", "[", "bsymb_", "]"}], " ", ":=", " ", 
   RowBox[{
    RowBox[{"Total", "[", 
     RowBox[{
      RowBox[{"Abs", "[", "bsymb", "]"}], "^", "2"}], "]"}], "/", 
    RowBox[{"Length", "[", "symb", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Fy", "[", 
    RowBox[{"y_", ",", "\[Sigma]_", ",", " ", "bsymb_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"1", "/", 
     RowBox[{"Length", "[", "bsymb", "]"}]}], 
    RowBox[{"1", "/", 
     RowBox[{"(", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"\[Pi]", "*", 
        RowBox[{"\[Sigma]", "^", "2"}]}], "]"}], ")"}]}], "*", 
    RowBox[{"Total", "[", 
     RowBox[{"Exp", "[", 
      RowBox[{
       RowBox[{"-", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"y", "-", "bsymb"}], ")"}], "^", "2"}]}], "/", 
       RowBox[{"(", 
        RowBox[{"\[Sigma]", "^", "2"}], ")"}]}], "]"}], "]"}]}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"Condexp", "[", 
    RowBox[{"y_", ",", "\[Sigma]_", ",", "bsymb_"}], "]"}], " ", ":=", " ", 
   RowBox[{
    RowBox[{"Total", "[", 
     RowBox[{"bsymb", "*", 
      RowBox[{"Exp", "[", 
       RowBox[{
        RowBox[{"-", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"y", "-", "bsymb"}], ")"}], "^", "2"}]}], "/", 
        RowBox[{"(", 
         RowBox[{"\[Sigma]", "^", "2"}], ")"}]}], "]"}]}], "]"}], "/", 
    RowBox[{"Total", "[", 
     RowBox[{"Exp", "[", 
      RowBox[{
       RowBox[{"-", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"y", "-", "bsymb"}], ")"}], "^", "2"}]}], "/", 
       RowBox[{"(", 
        RowBox[{"\[Sigma]", "^", "2"}], ")"}]}], "]"}], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"varPAM", "[", 
    RowBox[{"\[Sigma]_", ",", "bsymb_"}], "]"}], ":=", 
   RowBox[{"NIntegrate", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"Condexp", "[", 
        RowBox[{"y", ",", "\[Sigma]", ",", "bsymb"}], "]"}], "^", "2"}], " ", 
      RowBox[{"Fy", "[", 
       RowBox[{"y", ",", "\[Sigma]", ",", "bsymb"}], "]"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "\[Infinity]"}], ",", "\[Infinity]"}], "}"}], ",", 
     RowBox[{"PrecisionGoal", "\[Rule]", "15"}], ",", " ", 
     RowBox[{"Method", "\[Rule]", "\"\<DoubleExponential\>\""}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"varPAMout", "[", 
    RowBox[{"\[Sigma]_", ",", "bsymb_"}], "]"}], " ", ":=", 
   RowBox[{
    RowBox[{"symbpow", "[", "bsymb", "]"}], "-", 
    RowBox[{"varPAM", "[", 
     RowBox[{"\[Sigma]", ",", " ", "bsymb"}], "]"}]}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.518997627625*^9, 3.518997629046875*^9}, 
   3.518998096203125*^9, {3.51900905984375*^9, 3.51900919071875*^9}, 
   3.519013167*^9, {3.51901339775*^9, 3.519013493015625*^9}, {
   3.519013561828125*^9, 3.519013573609375*^9}, 3.51901363109375*^9, {
   3.519013663265625*^9, 3.519013665890625*^9}, {3.519081336265625*^9, 
   3.519081356296875*^9}, {3.5190814461875*^9, 3.51908145528125*^9}, 
   3.5190814895*^9, {3.51908153690625*^9, 3.51908157796875*^9}, {
   3.5190839600625*^9, 3.519083961234375*^9}, {3.51908406784375*^9, 
   3.519084069015625*^9}, 3.519084280875*^9, {3.519084593265625*^9, 
   3.519084600609375*^9}, {3.519085540671875*^9, 3.519085560828125*^9}, {
   3.519091074*^9, 3.519091103125*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{
                 RowBox[{
                  RowBox[{
                   RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{"//", "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
               "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}],
        "//"}], "//"}], "//"}], "//"}], "//"}], "//"}]], "Input",
 CellChangeTimes->{{3.519085792703125*^9, 3.51908579628125*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "2"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "1"}], ",", "1"}], "}"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".015", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.5190091944375*^9, 3.519009260421875*^9}, {
   3.51900951415625*^9, 3.519009539296875*^9}, {3.519010508546875*^9, 
   3.51901053921875*^9}, 3.5190108393125*^9, 3.519015123140625*^9, {
   3.519091603859375*^9, 3.51909175025*^9}, {3.519092115875*^9, 
   3.519092115953125*^9}, {3.519093338546875*^9, 3.51909336553125*^9}, 
   3.519093761015625*^9, 3.51909462015625*^9}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"powsym", " ", "=", " ", "2"}], ";", "  ", 
  RowBox[{"symb", " ", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1"}], ",", "1"}], "}"}]}], ";", " ", 
  RowBox[{"norm\[Sigma]", " ", "=", ".054777039225262"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"msein", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"varPAMout", "[", 
  RowBox[{"msein", ",", "symb"}], "]"}]}], "Input",
 CellChangeTimes->{{3.5194381846067266`*^9, 3.519438268988061*^9}, {
   3.519438392906246*^9, 3.51943841362604*^9}, {3.519438506489571*^9, 
   3.519438508161976*^9}, {3.519438633802638*^9, 3.5194386348541503`*^9}, 
   3.519438691625784*^9, 3.519438744451744*^9, 3.5194389822837296`*^9, {
   3.519442626133328*^9, 3.519442641004712*^9}}],

Cell[BoxData["0.000029990890711428797`"], "Output",
 CellChangeTimes->{3.519438271401531*^9, 3.5194384155688334`*^9, 
  3.519438509904482*^9, 3.5194386365565987`*^9, 3.519438692927656*^9, 
  3.5194387455433135`*^9, 3.519438985258006*^9, 3.5194426480548496`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{
                 RowBox[{
                  RowBox[{
                   RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{"//", "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
               "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}],
        "//"}], "//"}], "//"}], "//"}], "//"}], "//"}]], "Input",
 CellChangeTimes->{{3.5190151261875*^9, 3.519015129328125*^9}, 
   3.519085800703125*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "6"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "1"}], ",", "1"}], "}"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".005", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}], "\[IndentingNewLine]", "varoutList"}], "Input",
 CellChangeTimes->{{3.51909339021875*^9, 3.519093396921875*^9}, {
   3.51909350178125*^9, 3.51909351415625*^9}, {3.519093549015625*^9, 
   3.51909355021875*^9}, 3.51909376553125*^9, {3.51909427325*^9, 
   3.519094274859375*^9}, 3.519094604703125*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "6"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "3"}], ",", 
      RowBox[{"-", "1"}], ",", "1", ",", "3"}], "}"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".005", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}], "\[IndentingNewLine]", "varoutList"}], "Input",
 CellChangeTimes->{{3.51909354034375*^9, 3.519093553328125*^9}, {
  3.51909428128125*^9, 3.519094281515625*^9}, {3.51909460815625*^9, 
  3.519094613171875*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{
                 RowBox[{
                  RowBox[{
                   RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{"//", "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
               "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}],
        "//"}], "//"}], "//"}], "//"}], "//"}], "//"}]], "Input",
 CellChangeTimes->{{3.5190933786875*^9, 3.519093382734375*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "10"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "3"}], ",", 
      RowBox[{"-", "1"}], ",", "1", ",", "3"}], "}"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".003", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"varoutList", "/", "powsym"}]}], "Input",
 CellChangeTimes->{{3.519095499171875*^9, 3.519095518984375*^9}, {
  3.5190961389375*^9, 3.519096167953125*^9}, {3.519096215234375*^9, 
  3.519096216078125*^9}, {3.51909654*^9, 3.5190965450625*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{
                 RowBox[{
                  RowBox[{
                   RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{"//", "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
               "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}],
        "//"}], "//"}], "//"}], "//"}], "//"}], "//"}]], "Input",
 CellChangeTimes->{{3.51909543909375*^9, 3.519095442703125*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"powsym", " ", "=", " ", "20"}], ";", 
  RowBox[{"symb", " ", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "3"}], ",", 
     RowBox[{"-", "1"}], ",", "1", ",", "3"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"msetest", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{".0014", "powsym"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"varPAMout", "[", 
  RowBox[{"msetest", ",", "symb"}], "]"}]}], "Input",
 CellChangeTimes->{{3.519009277328125*^9, 3.519009445484375*^9}, {
   3.51900981565625*^9, 3.519009878546875*^9}, {3.5190099104375*^9, 
   3.519009913953125*^9}, {3.5190099506875*^9, 3.51900995896875*^9}, {
   3.519009996609375*^9, 3.519009998890625*^9}, {3.519010204375*^9, 
   3.51901030803125*^9}, 3.5190103859375*^9, {3.519081600859375*^9, 
   3.5190816409375*^9}, {3.519082584390625*^9, 3.519082592515625*^9}, {
   3.51908279109375*^9, 3.519082807875*^9}, {3.5190829285*^9, 
   3.51908301834375*^9}, 3.519083117171875*^9, {3.51908317884375*^9, 
   3.519083238*^9}, {3.51908329359375*^9, 3.519083299390625*^9}, 
   3.51908335290625*^9, 3.519083418234375*^9, 3.519083536*^9, {
   3.519083798984375*^9, 3.519083810609375*^9}, {3.519083842984375*^9, 
   3.51908384303125*^9}, {3.519083949234375*^9, 3.5190839549375*^9}, 
   3.51908400953125*^9, {3.519084273640625*^9, 3.519084291203125*^9}, {
   3.519084337390625*^9, 3.519084362234375*^9}, {3.519084509796875*^9, 
   3.51908464290625*^9}, {3.5190912606875*^9, 3.519091287015625*^9}, {
   3.51909342253125*^9, 3.51909343909375*^9}, {3.519093485875*^9, 
   3.519093489921875*^9}, {3.5190955274375*^9, 3.51909555340625*^9}, {
   3.519095589859375*^9, 3.519095633796875*^9}, {3.519095938171875*^9, 
   3.519096130171875*^9}, {3.51909753575*^9, 3.519097597578125*^9}, {
   3.519097663953125*^9, 3.519097675296875*^9}, {3.519097706671875*^9, 
   3.5190977085625*^9}}],

Cell[BoxData["3.552713678800501`*^-15"], "Output",
 CellChangeTimes->{{3.5190960254375*^9, 3.51909613065625*^9}, {
   3.519097541015625*^9, 3.519097593875*^9}, {3.5190976644375*^9, 
   3.519097676375*^9}, 3.5190977103125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"powsym", " ", "=", " ", "20"}], ";", 
  RowBox[{"symb", " ", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "5"}], ",", 
     RowBox[{"-", "3"}], ",", 
     RowBox[{"-", "1"}], ",", "1", ",", "3", ",", "5"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"msetest", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{".0014", "powsym"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"varPAMout", "[", 
  RowBox[{"msetest", ",", "symb"}], "]"}]}], "Input",
 CellChangeTimes->{{3.5190914805*^9, 3.5190914906875*^9}, {
  3.519093449046875*^9, 3.519093455171875*^9}, {3.51909760515625*^9, 
  3.519097704*^9}}],

Cell[BoxData["8.881784197001252`*^-15"], "Output",
 CellChangeTimes->{
  3.51909149284375*^9, 3.51909347096875*^9, {3.51909763959375*^9, 
   3.51909771290625*^9}}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "20"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "3"}], ",", 
      RowBox[{"-", "1"}], ",", "1", ",", "3"}], "}"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".0014", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"varoutList", "/", "powsym"}]}], "Input",
 CellChangeTimes->{{3.519097462046875*^9, 3.519097462078125*^9}, {
  3.51909773465625*^9, 3.519097734859375*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "20"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", 
      RowBox[{"-", "3"}], ",", 
      RowBox[{"-", "1"}], ",", "1", ",", "3", ",", "5"}], "}"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".0014", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"varoutList", "/", "powsym"}]}], "Input",
 CellChangeTimes->{{3.519097522703125*^9, 3.519097526875*^9}, {
  3.51909773878125*^9, 3.519097738953125*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{
                 RowBox[{
                  RowBox[{
                   RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{
                    RowBox[{"//", "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
                    "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], 
               "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}], "//"}],
        "//"}], "//"}], "//"}], "//"}], "//"}], "//"}]], "Input",
 CellChangeTimes->{{3.51909744984375*^9, 3.51909745371875*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"powsym", " ", "=", " ", "42"}], ";", 
  RowBox[{"symb", " ", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "7"}], ",", 
     RowBox[{"-", "5"}], ",", 
     RowBox[{"-", "3"}], ",", 
     RowBox[{"-", "1"}], ",", "1", ",", "3", ",", "5", ",", "7"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"msetest", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{".0008", "powsym"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"varPAMout", "[", 
  RowBox[{"msetest", ",", "symb"}], "]"}]}], "Input",
 CellChangeTimes->{{3.51909886675*^9, 3.51909887525*^9}, {3.51909890659375*^9,
   3.519099044625*^9}}],

Cell[BoxData["3.552713678800501`*^-14"], "Output",
 CellChangeTimes->{{3.51909891259375*^9, 3.51909904509375*^9}}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"powsym", " ", "=", " ", "42"}], ";", " ", 
   RowBox[{"symb", " ", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "7"}], ",", 
      RowBox[{"-", "5"}], ",", 
      RowBox[{"-", "3"}], ",", 
      RowBox[{"-", "1"}], ",", "1", ",", "3", ",", "5", ",", "7"}], "}"}]}], 
   ";"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"norm\[Sigma]List", " ", "=", "  ", 
   RowBox[{"Range", "[", 
    RowBox[{".0008", ",", "1.5", ",", " ", ".0001"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"mseinList", " ", "=", " ", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"powsym", "*", "norm\[Sigma]List"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"varoutList", " ", "=", " ", 
   RowBox[{"ConstantArray", "[", 
    RowBox[{"0", ",", 
     RowBox[{"Length", "[", "norm\[Sigma]List", "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "1"}], ",", 
   RowBox[{"i", "\[LessEqual]", 
    RowBox[{"Length", "[", "mseinList", "]"}]}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{"varoutList", "[", 
     RowBox[{"[", "i", "]"}], "]"}], "=", 
    RowBox[{"varPAMout", "[", 
     RowBox[{
      RowBox[{"mseinList", "[", 
       RowBox[{"[", "i", "]"}], "]"}], ",", "symb"}], "]"}]}]}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"varoutList", "/", "powsym"}]}], "Input",
 CellChangeTimes->{{3.51909889428125*^9, 3.519098909578125*^9}, {
  3.51909905228125*^9, 3.51909905259375*^9}}]
},
WindowSize->{1016, 651},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 26, 0, 31, "Input"],
Cell[574, 22, 3405, 92, 132, "Input"],
Cell[3982, 116, 1470, 46, 31, "Input"],
Cell[5455, 164, 1596, 43, 112, "Input"],
Cell[CellGroupData[{
Cell[7076, 211, 861, 20, 72, "Input"],
Cell[7940, 233, 261, 3, 30, "Output"]
}, Open  ]],
Cell[8216, 239, 1495, 47, 31, "Input"],
Cell[9714, 288, 1495, 41, 132, "Input"],
Cell[11212, 331, 1447, 41, 132, "Input"],
Cell[12662, 374, 1469, 46, 31, "Input"],
Cell[14134, 422, 1513, 42, 132, "Input"],
Cell[15650, 466, 1470, 46, 31, "Input"],
Cell[CellGroupData[{
Cell[17145, 516, 1894, 35, 72, "Input"],
Cell[19042, 553, 225, 3, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[19304, 561, 671, 18, 72, "Input"],
Cell[19978, 581, 163, 3, 30, "Output"]
}, Open  ]],
Cell[20156, 587, 1429, 41, 132, "Input"],
Cell[21588, 630, 1468, 42, 132, "Input"],
Cell[23059, 674, 1469, 46, 31, "Input"],
Cell[CellGroupData[{
Cell[24553, 724, 665, 18, 72, "Input"],
Cell[25221, 744, 114, 1, 30, "Output"]
}, Open  ]],
Cell[25350, 748, 1512, 43, 132, "Input"]
}
]
*)

(* End of internal cache information *)
